Question 31: EM waves

Question

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E}(x, t)=25 \sin \left(2.0 	imes 10^{15} t-10^7 xight) \hat{n}$ then the refractive index of the medium is $\_\_\_\_$ .
(All given measurement are in SI units)

Accepted Answer

The standard equation for a wave travelling in the +x direction is :
$$ \mathrm{E}(\mathrm{x}, \mathrm{t})=\mathrm{E}_0 \sin (\omega \mathrm{t}-\mathrm{kx}) $$
The given equation of electromagnetic wave is $\overrightarrow{\mathrm{E}}(\mathrm{x}, \mathrm{t})=25 \sin \left(2.0 	imes 10^{15} \mathrm{t}-10^7 \mathrm{x}ight) \hat{\mathrm{n}}$ :
Comparing both the equations,
Angular frequency $=\omega=2.0 	imes 10^{15} \mathrm{rad} / \mathrm{s}$
Wave number $=\mathrm{k}=10^7 \mathrm{~m}^{-1}$
The speed of the electromagnetic wave in the medium is given by the ratio of angular frequency to wave number:
$$ v=\frac{\omega}{k} $$
$$ \mathrm{v}=\frac{2.0 	imes 10^{15}}{10^7}=2.0 	imes 10^8 \mathrm{~m} / \mathrm{s} $$
The refractive index of a medium is the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v) :
$$ \mathrm{n}=\frac{\mathrm{c}}{\mathrm{v}} $$
Taking the speed of light in vacuum as $\mathrm{c}=3.0 	imes 10^8 \mathrm{~m} / \mathrm{s}$ :
$$ \mathrm{n}=\frac{3.0 	imes 10^8}{2.0 	imes 10^8} $$
$$ \mathrm{n}=1.5 $$
Hence, the correct option is (C).

Answer

2

Answer

1.2

Answer

1.5

Answer

1.7

EM waves

The electric field of an electromagnetic wave travelling through a medium is given by \vec{E}(x, t)=25 \sin \left(2.0 \times 10^{15} t-10^7 x\right) \hat{n} then the refractive index of the medium is \_\_\_\_ . (All given measurement are in SI units)

Choose the correct answer: